Problem: A certain food has a gluten ratio of $13\,\text{mg}$ of gluten per $\text{L}$ of the food. What is the gluten ratio in micrograms per milliliter $\left(\dfrac{\mu\text{g}}{\text{mL}}\right)$ ?
We will convert $13\,\dfrac{\text{mg}}{\text{L}}$ to a rate in $\dfrac{\mu\text{g}}{\text{mL}}$ using the following conversion rates: There are $1000\,\mu\text{g}$ per $1\text{ mg}$. There are $1000\text{ mL}$ per $1\text{ L}$. $\begin{aligned} &\phantom{=} \dfrac{13 \text{ mg}}{1\text{ L}} \cdot\dfrac{1000\,\mu\text{g}}{1\text{ mg}}\cdot\dfrac{1\text{ L}}{1000\text{ mL}} \\\\ &=\dfrac{13 \cdot 1000 \cdot 1 \cdot \cancel{\text{mg}}\cdot \mu\text{g} \cdot \cancel{\text{L}}}{1\cdot 1 \cdot 1000 \cdot\cancel{\text{L}}\cdot \cancel{\text{mg}} \cdot \text{mL} } \\\\ &=\dfrac{13{,}000}{1000}\,\dfrac{\mu\text{g}}{\text{mL}} \\\\ &=13\,\dfrac{\mu\text{g}}{\text{mL}} \end{aligned}$ In conclusion, the gluten ratio in $\dfrac{\mu\text{g}}{\text{mL}}$ is: $13\,\dfrac{\mu\text{g}}{\text{mL}}$